Processes of electric conduction and polarisation can be examined by the measurement of dielectric properties of the insulation. Test methods can be classified based on the measured physical property.
One possible classification is the following: some test methods examine the dielectric properties in the time domain, other ones in the frequency domain [32-34]. Another possible classification is this: which methods are able to determine properties of conduction and which ones are suitable for the determination of the properties of polarisation, how can the two processes be separated. Such classification can be seen in [35].
Fundamentals of different DC diagnostic methods can be easily followed according to Fig. 7.2, where the time function of the measured parameters can be seen.
Diagnostics of insulations
Fig. 7.2. Dielectric measurements in time domain [34]
Notation of parameters is the following.
Charging time: t ch; discharging time: t dp; self- (independent) discharging time: t idp, time between voltage zero and peak of return voltage t rmax; recording time of return voltage (t rvp).
Further parameters denoted in the figure:
1. Time function of polarising and depolarising currents (I p (t), I dp (t)) and their peak values (I pmax, I dpmax) 2. Times functions of charging voltage (U ch), discharging voltage (U d (t)) return voltage (U r (t)); peak value of
return voltage (U rmax),
3. Initial steepness of discharging and return voltage (S d and S r).
Taking into consideration the aforesaid parameters the most widely used evaluation methods for DC measurements are the following ones:
In case of AC tests the most widely used measurements are the following::
1. Loss factor at industrial frequency (50/60 Hz) 2. Loss factor at low frequencies
3. Loss factor measured by oscillating wave 4. Loss factor as a function of frequency (FDS).
Beyond the previous tests another widely used test method is the measurement of parameters of partial discharges formed inside the insulation or on the boundary surface of different insulating materials.
The most important difference between dielectric and partial discharge measurements is their content of information. Measurement of dielectric properties are based on the examination of dielectric and polarisation processes to estimate the actual condition of the insulation. Measurements of partial discharges give information about the insulator and not the insulating material, because the results of these measurements are influenced by the geometry, the environment of the insulator, the faults in the insulator, etc.
Furthermore, partial discharges are formed at local faults, thus it is not possible to estimate the overall condition and ageing of the insulation.
Thus, measurement of the parameters of partial discharges is very suitable for the determination of local faults.
Such measurement is the test with oscillating wave (OWTS) that is applied for high voltage cable lines nowadays [36]. Selectivity of the method is much better when the partial discharges are measured in an acoustic way. In this case the adequate position of faults (like the ones made during the installation of the cable) can be determined with high accuracy.
Significant advantage of the partial discharge measurement, that in most cases it is suitable for on-line tests.
A DC electromagnet pulls a contactor’s contacts if the current in its coil reaches 2.3 A. The rated voltage of the coil is 24 VDC , and its operating current is 2.9 A.
1. How much time does the electromagnet need to pull-in after turning on the circuit, if the coil’s inductance is 3.98 H?
2. How can this starting time be decreased to 1/5 of its original value, if the coil cannot be changed?
2. Example
I=12 kA steady-state fault current flows in a low voltage circuit supplied by V=230 V. The power factor of the circuit is cosυ=0.4, the frequency is f=50 Hz.
Determine the resistance (R) and inductance (L) of the circuit!
3. Example
I rms=50 kA steady-state fault current was measured in a circuit with cosυ=0.2. How much is the momentary value of the current at t=10 ms measured from the occurrence of the current, if
1. the fault current started at the moment of voltage zero?
2. the fault current begun at the steady-state current zero?
4. Example
How much permanent load current can be allowed, and how much is the temperature time constant, if the current flows in an infinite long copper bus bar with a cross sectional area of 100 ´ 10 mm, and the temperature rise allowed is τ max=60 K? (ρCu=2.27·10-8 Ωm, cv=3.38·106 Ws/m3K) Two arrangements are to be considered: the bus-bar is laid on its thinner, and on its wider edge. The film coefficient in case of smooth vertical surface and free convection is . If the surface is horizontal, it is half of the vertical case.
5. Example
The minimum interrupting current of an MCB is I h=14.5 A. The temperature of the bimetallic strip in the MCB had been equal with the ambient temperature, when a current of I r=24 A started flowing in the circuit. After t
r=69.5 s, the MCB interrupted the current.
Now, an ohmic load of P 0=1300 W has been connected to the circuit for a long time. How much will be the interruption time, if we turn on an additional electric motor with P=2.0 kW and cosυ=0.8? The supply voltage is V=230 V.
6. Example
How much is the maximum force between two parallel, filamentary conductor pieces, having equal length of l=3 m at a distance of R=10 cm (see figure below)? A usual current peak factor can be considered, and the rms quasi steady-state fault current is I st=12 kA.
Examples
7. Example
The constriction resistance between two contacts has been measured as function of the pressing force. Two corresponding points from the measurement:
F 1=15.8 N, R á1=6.01·10-5 Ω and F 2=8.0 N, R á2=7.54·10-5 Ω.
With a current of I=160 A, how much shall be the pressing force to reach the softening temperature (ϑ s=190°C) of the contact material, if a temperature of ϑ 0=77 °C was measured far from the constriction, and L=2,5×10-8 (V/K)2 ?
8. Example
Ideal interruption of a CB terminal fault in a circuit having serial and parallel damping:
cosυ=0.1; C=1 μF; R=200 mΩ; r=200 Ω;
1. How much is the voltage peak factor k peak=?
2. How much should r be, in order to get an aperiodic transient recovery voltage?